An Algorithm for Drawing General Undirected Graphs

Graphs (networks) are very common data structures which are handled in computers. Diagrams are widely used to represent the graph structures visually in many information systems. In order to automatically draw the diagrams which are, for example, state graphs, data-flow graphs, Petri nets, and entity-relationship diagrams, basic graph drawing algorithms are required. The state of the art in automatic drawing is surveyed comprehensively in [7,19]. There have been only a few algorithms for general undirected graphs. This paper presents a simple but successful algorithm for drawing undirected graphs and weighted graphs. The basic idea of our algorithm is as follows. We regard the desirable "geometric" (Euclidean) distance between two vertices in the drawing as the "graph theoretic" distance between them in the corresponding graph. We introduce a virtual dynamic system in which every two vertices are connected by a "spring" of such desirable length. Then, we regard the optimal layout of vertices as the state in which the total spring energy of the system is minimal. The "spring" idea for drawing general graphs was introduced in [6], and similar methods were used for drawing planar graphs with fixed boundary [2,20]. This paper brings a new significant result in graph drawing based on the spring model.